Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2024 MCQ for Mathematics of Computation is 1.78.

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Contents of Volume 72, Number 242
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Mixed finite volume methods on nonstaggered quadrilateral grids for elliptic problems: So-Hsiang Chou, Do Y. Kwak and Kwang Y. Kim;; Math. Comp. 72 (2003), 525-539; DOI: https://doi.org/10.1090/S0025-5718-02-01426-6; Published electronically: March 21, 2002; PDF

A mixed multiscale finite element method for elliptic problems with oscillating coefficients: Zhiming Chen and Thomas Y. Hou;; Math. Comp. 72 (2003), 541-576; DOI: https://doi.org/10.1090/S0025-5718-02-01441-2; Published electronically: June 28, 2002; HTML | PDF

Enhanced accuracy by post-processing for finite element methods for hyperbolic equations: Bernardo Cockburn, Mitchell Luskin, Chi-Wang Shu and Endre Süli;; Math. Comp. 72 (2003), 577-606; DOI: https://doi.org/10.1090/S0025-5718-02-01464-3; Published electronically: November 20, 2002; PDF

Finite element approximation of $H$-surfaces: Yuki Matsuzawa, Takashi Suzuki and Takuya Tsuchiya;; Math. Comp. 72 (2003), 607-617; DOI: https://doi.org/10.1090/S0025-5718-02-01447-3; Published electronically: October 22, 2002; PDF

Maximum norm stability of difference schemes for parabolic equations on overset nonmatching space-time grids: T. P. Mathew and G. Russo;; Math. Comp. 72 (2003), 619-656; DOI: https://doi.org/10.1090/S0025-5718-02-01462-X; Published electronically: November 4, 2002; PDF

Theoretical and numerical analysis for the quasi-continuum approximation of a material particle model: Ping Lin;; Math. Comp. 72 (2003), 657-675; DOI: https://doi.org/10.1090/S0025-5718-02-01456-4; Published electronically: June 4, 2002; PDF

Optimal a priori error bounds for the Rayleigh-Ritz method: Gerard L. G. Sleijpen, Jasper van den Eshof and Paul Smit;; Math. Comp. 72 (2003), 677-684; DOI: https://doi.org/10.1090/S0025-5718-02-01435-7; Published electronically: May 1, 2002; PDF

One-to-one piecewise linear mappings over triangulations: Michael S. Floater;; Math. Comp. 72 (2003), 685-696; DOI: https://doi.org/10.1090/S0025-5718-02-01466-7; Published electronically: October 17, 2002; PDF

About the sharpness of the stability estimates in the Kreiss matrix theorem: M. N. Spijker, S. Tracogna and B. D. Welfert;; Math. Comp. 72 (2003), 697-713; DOI: https://doi.org/10.1090/S0025-5718-02-01472-2; Published electronically: October 29, 2002; PDF

On perturbations of matrix pencils with real spectra, a revisit: Ren-Cang Li;; Math. Comp. 72 (2003), 715-728; DOI: https://doi.org/10.1090/S0025-5718-02-01449-7; Published electronically: May 16, 2002; PDF

Nyström-Clenshaw-Curtis quadrature for integral equations with discontinuous kernels: Sheon-Young Kang, Israel Koltracht and George Rawitscher;; Math. Comp. 72 (2003), 729-756; DOI: https://doi.org/10.1090/S0025-5718-02-01431-X; Published electronically: March 8, 2002; PDF

Existence verification for singular and nonsmooth zeros of real nonlinear systems: Jianwei Dian and R. Baker Kearfott;; Math. Comp. 72 (2003), 757-766; DOI: https://doi.org/10.1090/S0025-5718-02-01427-8; Published electronically: March 5, 2002; PDF

Near optimality of the sinc approximation: Masaaki Sugihara;; Math. Comp. 72 (2003), 767-786; DOI: https://doi.org/10.1090/S0025-5718-02-01451-5; Published electronically: June 4, 2002; PDF

Newman polynomials with prescribed vanishing and integer sets with distinct subset sums: Peter Borwein and Michael J. Mossinghoff;; Math. Comp. 72 (2003), 787-800; DOI: https://doi.org/10.1090/S0025-5718-02-01460-6; Published electronically: July 15, 2002; PDF

Factoring multivariate polynomials via partial differential equations: Shuhong Gao;; Math. Comp. 72 (2003), 801-822; DOI: https://doi.org/10.1090/S0025-5718-02-01428-X; Published electronically: February 28, 2002; PDF

Strong tractability of multivariate integration using quasi–Monte Carlo algorithms: Xiaoqun Wang;; Math. Comp. 72 (2003), 823-838; DOI: https://doi.org/10.1090/S0025-5718-02-01440-0; Published electronically: June 25, 2002; PDF

A mass formula for unimodular lattices with no roots: Oliver D. King;; Math. Comp. 72 (2003), 839-863; DOI: https://doi.org/10.1090/S0025-5718-02-01455-2; Published electronically: June 25, 2002; PDF

Relative invariants of some 2-simple prehomogeneous vector spaces: Takeyoshi Kogiso, Go Miyabe, Miyuki Kobayashi and Tatsuo Kimura;; Math. Comp. 72 (2003), 865-889; DOI: https://doi.org/10.1090/S0025-5718-02-01470-9; Published electronically: October 18, 2002; PDF

Nontrivial Galois module structure of cyclotomic fields: Marc Conrad and Daniel R. Replogle;; Math. Comp. 72 (2003), 891-899; DOI: https://doi.org/10.1090/S0025-5718-02-01457-6; Published electronically: June 4, 2002; PDF

On the linear independence measure of logarithms of rational numbers: Qiang Wu;; Math. Comp. 72 (2003), 901-911; DOI: https://doi.org/10.1090/S0025-5718-02-01442-4; Published electronically: June 25, 2002; PDF

Class numbers of real cyclotomic fields of prime conductor: René Schoof;; Math. Comp. 72 (2003), 913-937; DOI: https://doi.org/10.1090/S0025-5718-02-01432-1; Published electronically: February 15, 2002; PDF

The first known type $(7,1)$ amicable pair: Mariano Garcia;; Math. Comp. 72 (2003), 939-940; DOI: https://doi.org/10.1090/S0025-5718-02-01450-3; Published electronically: May 15, 2002; PDF

Constructing complete tables of quartic fields using Kummer theory: Henri Cohen, Francisco Diaz y Diaz and Michel Olivier;; Math. Comp. 72 (2003), 941-951; DOI: https://doi.org/10.1090/S0025-5718-02-01452-7; Published electronically: June 13, 2002; PDF

Improvements to the general number field sieve for discrete logarithms in prime fields. A comparison with the gaussian integer method: Antoine Joux and Reynald Lercier;; Math. Comp. 72 (2003), 953-967; DOI: https://doi.org/10.1090/S0025-5718-02-01482-5; Published electronically: November 4, 2002; PDF

A computation of minimal polynomials of special values of Siegel modular functions: Tsuyoshi Itoh;; Math. Comp. 72 (2003), 969-973; DOI: https://doi.org/10.1090/S0025-5718-02-01430-8; Published electronically: March 22, 2002; PDF

Pseudozeros of multivariate polynomials: J. William Hoffman, James J. Madden and Hong Zhang;; Math. Comp. 72 (2003), 975-1002; DOI: https://doi.org/10.1090/S0025-5718-02-01429-1; Published electronically: May 15, 2002; PDF

The class number one problem for some non-abelian normal CM-fields of degree 48: Ku-Young Chang and Soun-Hi Kwon;; Math. Comp. 72 (2003), 1003-1017; DOI: https://doi.org/10.1090/S0025-5718-02-01443-6; Published electronically: October 17, 2002; PDF

Linear quintuple-product identities: Richard Blecksmith and John Brillhart;; Math. Comp. 72 (2003), 1019-1033; DOI: https://doi.org/10.1090/S0025-5718-02-01461-8; Published electronically: August 14, 2002; PDF

Lower bounds for the total stopping time of $3x + 1$ iterates: David Applegate and Jeffrey C. Lagarias;; Math. Comp. 72 (2003), 1035-1049; DOI: https://doi.org/10.1090/S0025-5718-02-01425-4; Published electronically: June 6, 2002; PDF

The smallest solutions to the diophantine equation $x^6+y^6=a^6+b^6+c^6+d^6+e^6$: Giovanni Resta and Jean-Charles Meyrignac;; Math. Comp. 72 (2003), 1051-1054; DOI: https://doi.org/10.1090/S0025-5718-02-01445-X; Published electronically: June 6, 2002; PDF

Book Reviews
Book reviews do not contain an abstract. You may download each review in this issue using the links below.

Asymptotic approximations of integrals, by R. Wong.
Collected lectures on the preservation of stability under discretization, edited by D. Estep and S. Tavener.: Reviewer: Nico M Temme
Reviewer: John Strikwerda; Review information PDF; Math. Comp. 72 (2003), 1055-1056